Question

Define the following propositions: .p: You drive over 65 miles per hour q You get a speeding ticket Translate the following English sentence into logical expressions using the definitions above (a) You drive over 65 miles per hour, but you do not get a speeding ticket. (b) If you do not drive over 65 miles per hour, then you will not get a speeding ticket (c) You get a speeding ticket, but you did not drive over 65 miles per hour.

Answer 1

(a)
`p \wedge -q`

(b)
`\\eg p \Rightarrow \\eg q`

(c)
`q \wedge -p`

Explanation:

(a) You drive over 65 miles per hour, but you do not get a speeding ticket, it can be represented by:
`p \wedge -q`

(b) If you do not drive over 65 miles per hour, then you will not get a speeding ticket, it can be represented by:
`\\eg p \Rightarrow \\eg q`

(c) You get a speeding ticket, but you did not drive over 65 miles per hour, can be represented by:
`q \wedge -p`